The 74HC14 is simply being used to invert and buffer the A and B signals coming from the HEDR-8000. Each signal gets inverted once with a single inverter, then the output from that goes in parallel to another pair of inverters (which will inverter the signal back again to its original polarity), whose output are again paralleled and go out to the pin header. I suspect they're paralleling a pair of inverters for output so that the signal has a strong drive strength. Possibly it passes over a long cable harness, or whatever is receiving needs a low-impedance signal.
The 24C32 is an I2C 4KB EEPROM, and most probably just used for identification and/or serialisation of the module. It should have no impact on the sensing function of the module other than perhaps the main unit may refuse to operate if it can't interrogate the EEPROM to find out whether the encoder is present and/or what it is.
You can test the EEPROM by hooking up the VCC, GND, SDA, SCL pins on the header to something like a Raspberry Pi or Arduino and trying to read out its contents over I2C. From the way the A* pins are wired, the slave address for it should be 0x54.
The two resistors test great and are both 100kOhm +/- 1%
These are pull-up resistors for the I2C SDA and SCL lines. Bit odd to have such a high value of 100k, as normally they're <10k, but maybe the main unit has its own pull-ups, and these are just fail-safes.
The part of concern is the unknown part. It's a ceramic part, assuming its a capacitor but unknown value. It goes across the GND and VCC pins (Pin 4/5) of the HEDR-8000 which I believe is the 2K4 model.
I would say it's almost certainly just a decoupling capacitor, probably of same value as the other one - 100nF.
The datasheet for the HEDR-8000 doesn't mention the need for any other external components apart from a 220-ohm current-limiting resistor for the LED (which curiously is not featured on the PCB at all!), so it's unlikely to be anything else.
2) What kind of tests can I do on these specific chips to determine if they are good or not? Or should I just do a full test at the end and if it works...it works.
3) Expecting 90 deg phase shift between A/B on scope (with A leading). The input on this PCB is 5v but what are the expected outputs on this circuit? Also 0-5v on the scope from Channel A / B?
I would try to do an end-to-end test. It should be fairly simple with a 'scope and multimeter to determine whether the module is functioning. You should be able to do it on the bench by just providing a 5V power supply. I would go about it as follows:
1. Check whether the LED in the encoder is illuminating. Jump between VLED and 5V with a 220-ohm resistor, and see if it lights. Datasheet doesn't say whether it might be a non-visible infrared LED, so if no light appears, check with camera (e.g. smartphone) to see if it lights - IR LEDs usually can be seen to glow dim purple-ish colour on camera screen. If LED is bad, you need a new HEDR-8000.
2. With the 5V powered and the LED illuminated, try to replicate the encoder wheel pattern in some kind of to-hand medium (e.g. cut some holes in paper - dimensions given in the datasheet) and see what signals you get out of the A and B pins of the HEDR-8000. The datasheet says they should have a high level at least 2.4V. No signal? Again, possibly bad HEDR-8000.
3. If you get what's expected there, then move to probe the 74HC14 input pins and see if the same signal appears. Then move to the 74HC14 outputs and check again for a signal. No output signal? Replace the 74HC14. Outputs from the inverter should have a high level around 4-5V.
4. Check the EEPROM functions and seems to contain valid data - as described above.
Other than those things, there's not really much else to go wrong. This module is pretty simple.